具有免疫应答和吸收效应的病毒感染模型分析

Analysis for Viral Infection Model with Absorption and Immune Response

研究了具有免疫应答和吸收效应的病毒动力学模型的动力学行为.通过构造适当的Lyapunov泛函,使用LaSalle不变性原理,证明了基本再生数、CTL免疫再生数、抗体免疫再生数、CTL免疫竞争再生数和抗体免疫竞争再生数决定了模型的全局性态.若基本再生数小于等于1,病毒在体内清除.若基本再生数大于1,正解在满足条件max{R_(1),R_(2)}<1<R_(0)<P_(0)时趋于无免疫平衡点,在满足条件R_(4)≤1<R_(1)<R_(0)<P_(0)时趋于CTL主导平衡点,在满足条件R3≤1<R_(2)<R_(0)<P_(0)时趋于抗体主导平衡点,在满足条件1<R_(3)<R_(0)<P_(3),1<R_(4)<R_(0)<P_(3)时趋于正平衡点,据此获得了无病平衡点、无免疫平衡点、CTL主导平衡点、抗体主导平衡点和正平衡点全局渐近稳定的充分条件,推广了Dominik(2003)的工作.

In this paper,the dynamical behaviors of the virus dynamics model with immune response and absorption are studied.By constructing suitable Lyapunov functionals,using the LaSalle invariance principle,have shown that basic reproductive number,CTL immune response reproductive number and antibody immune response reproductive number,CTL immune response competition reproductive number,antibody immune response competition reproductive number determine the global properties of the model.If the basic reproduction number is less than or equal to 1,the virus is cleared.For the basic reproduction number is greater than 1,positive solutions approach to an immune-free equilibrium if conditions are met max{R_(1),R_(2)}≤1<<R_(0)<P_(0),to a CTLdominant equilibrium if conditions are met R_(4)≤1<R_(1)<R_(0)<P_(0),to a antibody dominant equilibrium if conditions are met R_(3)≤1<R_(2)<R_(0)<P_(0),and to an endemic equilibrium conditions are met 1<R_(3)<R_(0)<P_(3),1<R_(4)<R_(0)<P_(3),obtained the sufficient conditions of the global stability of the infection-free equilibrium,the immune-free equilibrium,the CTL dominant equilibrium,the antibody dominant equilibrium and the positive equilibrium,generalized the work of Dominik(2003).